A numerical investigation of coorbital stability and libration in three dimensions

TL;DR

This paper numerically investigates the stability and libration of coorbital resonance in three dimensions, revealing new modes and the robustness of coorbital stability across all inclinations, including retrograde and polar orbits.

Contribution

It introduces new coorbital modes in three dimensions and demonstrates the stability of coorbital resonance at all inclinations, expanding understanding beyond planar cases.

Findings

Retrograde mode I (R1) and mode II (R2) persist with inclination changes.

A new 3D coorbital mode (R4) appears, analogous to horseshoe orbits.

Coorbital resonance remains stable at all inclinations, including retrograde and polar.

Abstract

Motivated by the dynamics of resonance capture, we study numerically the coorbital resonance for inclination180 >=I>=0 in the circular restricted three-body problem. We examine the similarities and differences between planar and three dimensional coorbital resonance capture and seek their origin in the stability of coorbital motion at arbitrary inclination. After we present stability maps of the planar prograde and retrograde coorbital resonances, we characterize the new coorbital modes in three dimensions. We see that retrograde mode I (R1) and mode II (R2) persist as we change the relative inclination, while retrograde mode III (R3) seems to exist only in the planar problem. A new coorbital mode (R4) appears in 3D which is a retrograde analogue to an horseshoe-orbit. The Kozai-Lidov resonance is active for retrograde orbits as well as prograde orbits and plays a key role in coorbital resonance capture. Stable coorbital modes exist at all inclinations, including retrograde and polar obits. This result confirms the robustness the coorbital resonance at large inclination and encourages the search for retrograde coorbital companions of the solar system's planets.